News — , , and Erik S酶rensen are condensed matter physicists. They study exotic but tangible systems, such as superfluids. And their latest paper about one such system has a black hole in it.
How did a black hole get into a condensed matter paper? 鈥淲ell, it鈥檚 a long story,鈥� says Sachdev, who is a professor at Harvard and a at .
It鈥檚 a long story, he might add, that in a way starts with him: he was one of the first condensed matter physicists to venture into the strange land of string theory, where the black holes live. But that is getting ahead of the tale.
鈥淟et鈥檚 start here,鈥� Sachdev says. 鈥淐ondensed matter physicists study the behaviour of electrons in many materials 鈥� semiconductors, metals, and exotic materials like superconductors.鈥�
Normally, these physicists can model the behaviour of a material as if electrons were moving freely around inside it. Even if that鈥檚 not what鈥檚 actually happening, because of complex interactions, it makes the model easy to understand and the calculations easier to do. Electrons (and occasionally other particles) used in this kind of short-hand model are called quasi-particles.
However, there are a handful of systems that cannot be described by considering electrons (or any other kind of quasi-particle) moving around.
鈥淲hat we try to do is understand a quantum system where you have electricity without electrons,鈥� says Sachdev. 鈥淥f course, the system does have electrons in it, but the behaviour of the system doesn鈥檛 look like electrons moving at all. What you see is not even particles, but some lumps of quantum excitations that are doing strange quantum things.鈥�
鈥淲ithout quasi-particles, it鈥檚 a mess,鈥� says William Witczak-Krempa. Witczak-Krempa, a Perimeter postdoctoral fellow, is also a condensed matter theorist who collaborated with Sachdev on the paper. 鈥淚t鈥檚 this quantum fuzzball of stuff.鈥�
Describing such a fuzzball system is a challenge 鈥� but it鈥檚 crucial to understanding many modern materials, including and . The broad problem of how to model systems without quasi-particles has been stumping condensed matter theorists for decades.
鈥淲hat we decided to do was look at a simple case of such an electricity-without-electrons system,鈥� says Witczak-Krempa. 鈥淭hat turns out to be a quantum phase transition between a superfluid and an insulator.鈥�
A fair amount of work had been done on such systems, such that the team was able to make progress modelling the system using the traditional mathematical tools of condensed matter. Sachdev and Witczak-Krempa worked with Erik S酶rensen of McMaster University on this aspect of their paper. S酶rensen used a computer simulation 鈥� specifically, a quantum Monte Carlo simulation 鈥� to predict how conductivity should change with temperature and frequency as a superfluid turns into an insulator.
鈥淭his frequency dependence tells us how the quantum fluid behaves in time. This dynamic behaviour is notoriously hard to study using standard methods, including quantum Monte Carlo simulations,鈥� says Witczak-Krempa. 鈥淓rik鈥檚 work was a huge computational achievement. It took months of processing time. And, in the end, the results still needed to be converted into a form that can be compared with experiments. This is where we tried something new.鈥�
To perform this conversion, Sachdev and Witczak-Krempa tackled the same system from a different angle: string theory. (Here, they build on Sachdev鈥檚 previous work with Perimeter Faculty member and one of his graduate students, Ajay Singh.)One of the pillars of string theory is that certain quantum field theories (technically known as conformal field theories) can be translated into a theory of gravity with one extra dimension.
Sachdev explains where the extra dimension comes in. Wiggling his fingers above the tabletop, he conjures strings moving through the air.
鈥淚n certain configurations, the strings all end on a kind of membrane,鈥� he says, tapping his fingertips on the table鈥檚 surface. 鈥淵ou might ask yourself: if you were living on the membrane [the table surface] 鈥� and you didn鈥檛 know about the extra dimensions where the strings were, what would you see?鈥�
He answers himself: 鈥淥nly the ends of the strings. They would look like particles. What鈥檚 amazing is that string theorists found that the theories that you鈥檇 use to define the ends of the strings on the membrane are remarkably like the theory we want to use to describe our system.鈥�
The quantum field theory describing Sachdev and Witczak-Krempa鈥檚 鈥渇uzzball鈥� system shares many fundamental properties with the conformal field theories associated with string theory 鈥� so many that the researchers were able to map the two-dimensional field theory into a three-dimensional theory of gravity.
鈥淲e ended up studying the physics of this alternate reality,鈥� says Witczak-Krempa. 鈥淯sing this technique, we were able to translate a very hard problem into a fairly easy one.鈥滱lbeit a fairly easy problem involving a black hole.
鈥淲e wanted to look at the physics of the boundary 鈥� the physics at the table top,鈥� says Witczak-Krempa. 鈥淏ut we wanted to heat it up a bit 鈥� give it a finite temperature. It turns out that the natural way of doing this is to invoke a black hole.鈥漅eally?
鈥淭here are various ways of developing an intuition about that,鈥� he says. 鈥淔or instance, you can remember that the black hole will release Hawking radiation. The Hawking radiation escapes and eventually hits the boundary where the system lives, and heats it up.鈥�
Witczak-Krempa admits it鈥檚 unorthodox: 鈥淢ost condensed matter people would go: 鈥榃hy is there a black hole in this paper?鈥� It鈥檚 crazy. But what鈥檚 even crazier is that this mathematical machinery works quite well. It gives you answers that make a lot of sense. You can compare them directly with Erik鈥檚 Monte Carlo results, and they check out.鈥�
It鈥檚 the first time results from a traditional large-scale condensed matter simulation have been compared to results from the new string theory approach.
Sachdev is cautiously thrilled: 鈥淭here are a couple of issues we don鈥檛 fully understand and one discrepancy we wish we understood better, but in general it鈥檚 worked extremely well. It鈥檚 progress on something I鈥檝e been thinking about for more than 20 years. And now we finally have a theory that is perhaps not complete, but is encouragingly successful.鈥�
What鈥檚 more, string theory has finally produced a set of physical predictions that experimentalists can go check. Sachdev and Witczak-Krempa are hoping that an experimental team will try soon.
鈥淟et鈥檚 see what happens,鈥� says Sachdev. 鈥淲e鈥檙e pushing string theory to a new regime. Whatever happens, we will learn more.鈥�
The new paper was published yesterday in .
FURTHER EXPLORATION鈥� 鈥� Read three papers that this works builds upon (on arXiv): - - -
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